Trusts and trust law is complex.
Agreed, I'm about to set one up and settle some cash in it.
the actual owners of the aircraft are quite entitled to “file” a charge over the asset
That's a tautology:-
I refer m'learned friend to
FAR 47.5
(b) An aircraft may be registered only by and in the legal name of its owner.
ergo, if the registration is valid "the actual owners of the aircraft " are the US entity, not you.